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研究生： 周培頌
Peh-Sung Chou
論文名稱： 濃度調變對單向固化形態穩定的影響
The effect of concentration modulation on morphological instability of a binary alloy
指導教授： 鍾志昂
Chih-Ang Chung
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 92
語文別： 中文
論文頁數： 63
中文關鍵詞： 固化 、調變 、線性穩定分析 、形態不穩定 、同步模態 、次調和模態
外文關鍵詞： subharmonic, synchronous, morphological instability, modulation, solidification, linear stability analysis
相關次數： 點閱：12  下載：0 
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    • 單向固化製程中合金的缺陷產生原因，與固化過程中在固液介面的過冷現象有關。近幾年來商品朝著輕薄短小發展,造成對固化過程缺陷控制要求的嚴苛，合金固化因此受到許多學者廣泛的研究。
    為了改善這種缺陷的情況，本文將模擬鉛-錫單向固化合金流場，研究在固液介面形態的變化情形，並嘗試經由控制某些特定參數，來分析對固液介面形態不穩定(morphological instability)的影響，藉由對單向固化流場作濃度週期性調變，探討基態系統的變化，利用解析解的方法求解基態；接著對基態流場作線性穩定分析，就同步及次調和兩種不穩定模態來探討固液介面的形態不穩定現象。

    We study the morphological instability of the melt-solid interface of a dilute binary alloy. The alloy is assumed to undergo directional solidification into a modulated solutal field. Under such a circumstance, the molten zone is oscillated back and forth in a periodic way. The basic state is solved analytically assuming the melt-solid interface is flat and the bulk melt is quiescent by expanding the governing equation in terms of the assumed infinitesimal modulation amplitude. By further neglecting the flow field, we investigate the interfacial stability of the base state by considering two specific instability modes: the synchronous and subharmonic modes. The synchronous modes vary with time having the same frequency as that of the oscillatory molten zone, while the sudharmonic modes are of the half frequency.

    摘要 目錄 圖目錄 符號說明 第一章 序論 1 1.1前言 1 1.2文獻回顧 1 1.3研究動機 3 第二章 濃度週期性調變下之基態流場 5 2.1問題描述及統御方程式 5 2.2無因次化 7 2.3基態解 8 2.3.1解基態濃度 及固液介面高度 9 2.3.2按照δ的階數整理 9 2.4基態系統分析 15 2.4.1 與基態系統關係 15 2.4.2 與基態系統關係 15 第三章 濃度週期性調變之線性穩定分析 17 3.1線性擾動方程式 17 3.2線性擾動方程式之求解 22 3.3線性穩定分析之應用 26 3.3.1同步模態 27 3.3.2次調和模態 29 3.4數值方法 30 3.5數值計算結果 31 第四章 結論與展望 34 參考文獻 37 附錄一 鉛錫合金物理參數 40 附錄二 Mathematica計算之結果 41

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